Working Paper: CEPR ID: DP5645
Authors: Kai A. Konrad; Dan Kovenock
Abstract: We study equilibrium in a multistage race in which players compete in a sequence of simultaneous move component contests. Players may win a prize for winning each component contest, as well as a prize for winning the overall race. Each component contest is an all-pay auction with complete information. We characterize the unique equilibrium analytically and demonstrate that it exhibits endogenous uncertainty. Even a large lead by one player does not fully discourage the other player, and each feasible state is reached with positive probability in equilibrium (pervasiveness). Total effort may exceed the value of the prize by a factor that is proportional to the maximum number of stages. Important applications are to war, sports, and R&D contests and the results have empirical counterparts there.
Keywords: allpay auction; conflict; contest; discouragement; endogenous uncertainty; multistage; preemption; R&D; race
JEL Codes: D72; D74
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Winning a component contest (C) (Y60) | Player's probability of winning the overall contest (O) (C72) |
| Winning a component contest (C) (Y60) | Intermediate prize (P) (D41) |
| Intermediate prize (P) (D41) | Future efforts (E) (I25) |
| Total effort (TE) (A39) | Structure of the contest (D44) |
| Winning a component contest (C) (Y60) | Player's future efforts (E) (Z22) |